Have you ever had a difficult time choosing options for a sandwich? Take a look at this dilemma.
For a sub sandwich, Luis has the following choices.
How many different kinds of sandwiches can Luis make?
One way of figuring this out is to use a tree diagram. By the end of the Concept, you will know how to help Luis with this dilemma.
Guidance
Probability is a mathematical way of calculating how likely an event is likely to occur.
An event is a result of an experiment or activity that might include such things as:
 flipping a coin
 spinning a spinner
 rolling a number cube
 choosing an item from a jar or bag
An important concept when calculating probability is to think about outcomes.
An outcome is a possible result of some event occurring. When you flip a coin, “heads” is one outcome; tails is a second outcome.
Total outcomes are computed simply by counting all possible outcomes.
That is a great question.
One good way to count the total number of outcomes for an event is to make a tree diagram .
A tree diagram is a branching diagram that shows all possible outcomes for an event.
For instance, if you flip a coin two times, how many different outcomes are possible? To find out, make a tree diagram.
To make a tree diagram, split the different events into eitheror choices. The first choice breaks flip 1 down into heads or tails. Each outcome of flip 1 is broken down again for flip 2.
The pink box shows the total number of outcomes for both flips:
What happens when you increase the number of flips to three? Just add another section to your tree diagram.
In all, there are now 8 total outcomes.
Use a tree diagram to calculate the total possible outcomes.
Example A
A car has four seats. How many different options are there if three people ride in the car?
Solution: options.
Example B
Candice has two skirts, three shirts and two different sweaters. How many possible outfits can she create?
Solution: options.
Example C
Sam is trying to create a pizza. He has two crust options, four different cheese options and 8 different toppings to choose from. How many pizzas can he make if he only chooses one topping?
Solution: options.
Now let's go back to the dilemma from the beginning of the Concept.
To figure this out, Luis can create a tree diagram to show all of his choices and calculate the sandwich outcomes.
You can see that the tree diagram begins with the bread choices, then adds the second layer of the cheese options, and finally adds the meat choices.
There are twelve possible sandwich outcomes for Luis.
Vocabulary
 Probability
 the mathematical way of calculating the likelihood of an event occurring, the ratio of favorable outcomes to total outcomes.
 Event
 a result of an experiment or activity.
 Outcome
 a possible result of an event occurring.
 Tree Diagram
 a branching diagram that shows all possible outcomes for an event.
Guided Practice
Here is one for you to try on your own.
How many possibilities are there for a winwinwin?
Solution
You can see that when we break out all of the options that there is one chance for a winwinwin.
Video Review
Practice
Directions: Use a tree diagram to figure out all of the different outcomes.
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The
Gotham Gazette
offers the following newspaper choices:
 home or office delivery
 weekdays only, weekends only, or all seven day delivery
 monthly or weekly payments
How many different kinds of choices can you get?
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 cone: sugar, waffle
 size: teeny, mega, huge
 flavors: shocking blueberry, marvelous mango, chocolate attack
How many different choices are there?
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 What if Jessie has two sweaters, three turtlenecks and three jackets. How many possible combinations are there?
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 What if Jessie has three sweaters, two turtlenecks, two scarfs and three jackets. How many possible combinations are there?
 What if Jessie has four sweaters, two turtlenecks, two scarfs and three jackets. How many possible combinations are there?